in Definitions REF  and REF , using the belief update \(\psi ^{(q)}\)  which makes \(l(\xi ;O,{\tilde{q}})\)  prequentially additive. Now take \(I_1=(O^{(1)},\pi _0)\) , \(I_2=(O^{(2)},{\tilde{q}}_1)\)  and \(I=(O,\pi _0)\)  in the proof page 3 of the supplement to [1]}. We go through this to make it clear that everthing continues to fall into place and the presence of \({\tilde{q}}_1\)  inside the information \(I_2\)  is just what we need to make things work. We should keep in mind below that that \(\pi _0\)  and \({\tilde{q}}_1\)  are fixed pieces of information inside \(I_1\)  and \(I_2\)  as \(p\)  is varied.
